Definition

In terms of the standard coordinates(xμ)μ=0p(x^\mu)_{\mu = 0}^p on ℝp+1\mathbb{R}^{p+1} the Minkowski metric is the constant rank 2-tensor which is given by the diagonal matrixη=diag(−1,+1,+1,⋯,+1)\eta = diag(-1,+1,+1, \cdots , +1) (or else η=diag(+1,−1,−1,⋯,−1)\eta = diag(+1,-1,-1, \cdots, -1)).

This means that for v=(vμ)μ=0p∈ℝp,1v = (v^\mu)_{\mu = 0}^p \in \mathbb{R}^{p,1} then